Efficient Test to Demonstrate Genuine Three Particle Nonlocality

TL;DR

This paper introduces a new Bell-type inequality that more efficiently detects genuine tripartite nonlocality in quantum states compared to Svetlichny inequality, applicable to both pure and mixed states.

Contribution

The study proposes and validates a new inequality for detecting tripartite nonlocality, demonstrating its superiority over Svetlichny inequality for specific quantum states.

Findings

The new inequality outperforms Svetlichny inequality in revealing nonlocality.

It is effective for both pure and mixed entangled states.

Discord monogamy score can sometimes better measure quantum correlation than Svetlichny inequality.

Abstract

According to the studies of genuine tripartite nonlocality in discrete variable quantum systems conducted so far, Svetlichny inequality is considered as the best Bell-type inequality to detect genuine (three way) nonlocality of pure tripartite genuine entangled states. In the present work, we have considered another Bell-type inequality (which has been reported as the $99$-th facet of $NS_2$ local polytope in (J.-D. Bancal, et.al.,Phys. Rev.A \textbf{88}, 014102 (2013)), to reveal genuine tripartite nonlocality of generalized GHZ(Greenberger-Horne-Zeilinger) class and a subclass of extended GHZ class states(\cite{ACN}) thereby proving the conjecture given by Bancal, et.al.\cite{BAL} for the GGHZ class and the subclass of extended GHZ states. We compare the violation of this inequality with Svetlichny inequality which reveals the efficiency of the former inequality over the latter to demonstrate genuine nonlocality using the above classes of quantum states. Even in some cases discord monogamy score can be used as a better measure of quantum correlation over Svetlichny inequality for those classes of pure states. Besides, the $99$-th facet inequality is found efficient not only for revealing genuine nonlocal behavior of correlations emerging in systems using pure entangled states but also in some cases of mixed entangled states over Svetlichny inequality and some well known measures of entanglement .